Simplify the following expression and express the answer in scientific notation: (0.81 × 10⁻⁵) / (2.28…

Question

Simplify the following expression and express the answer in scientific notation: (0.81 × 10⁻⁵) / (2.28 × 10⁻⁷)

ScanSolve AI Tutor · Accepted Answer

Step 1: Write the given expression. (0.81 × 10⁻⁵)/(2.28 × 10⁻⁷) Step 2: Separate the numerical coefficients and the powers of 10. (0.81/2.28) × ((10⁻⁵)/(10⁻⁷)) Step 3: Calculate the division of the numerical coefficients. 0.81/2.28 ≈ 0.35526315789 Step 4: Calculate the division of the powers of 10 using the rule (a^m)/(aⁿ) = a^(m−n). (10⁻⁵)/(10⁻⁷) = 10⁻⁵⁻⁽⁻⁷⁾ = 10⁻⁵⁺⁷ = 10² Step 5: Multiply the results from Step 3 and Step 4. 0.35526315789 × 10² = 35.526315789 Step 6: Round the answer to an appropriate number of significant figures. The number 0.81 has 2 significant figures, and 2.28 has 3 significant figures. The result should be rounded to the least number of significant figures, which is 2. 35.526315789 ≈ 36 Step 7: Express the final answer in scientific notation. 36 = 3.6 × 10¹ The final answer is 3.6 × 10¹.

Simplify the following expression and express the answer in scientific notation: (0.81 x 10⁻⁵) / (2.28 x 10⁻⁷)

Answer

Step-by-step solution

Write the given expression.

Separate the numerical coefficients and the powers of 10.

Calculate the division of the numerical coefficients.

Calculate the division of the powers of 10 using the rule $\frac{a^m}{a^n} = a^{m-n}$ .

Multiply the results from Step 3 and Step 4.

Round the answer to an appropriate number of significant figures.

Express the final answer in scientific notation.

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